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Global stabilisation of linear systems with bounded controls by nonlinear feedback

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2 Author(s)
Zhou, B. ; Center for Control Theor. & Guidance Technol., Harbin Inst. of Technol., Harbin ; Duan, G.-R.

A general nonlinear feedback law for global stabilisation of asymptotically null controllable linear systems with bounded controls is established. It is shown that such a nonlinear feedback law can be constructed in two recursive ways. The results effectively allow for the construction of a hybrid control law which is partly of a nested saturation form and partly of a sum of saturations form, giving more flexibility to the designer. Using the recursive formulation, one can obtain a series of control laws containing the well-known nested type and parallel connections type laws as two special cases. Moreover, the eigenvalues corresponding to the linearised closed-loop system can be arbitrarily assigned within a certain region, which can be further used to improve the system performances. The possible ranges for the controller's parameters are extended with respect to existing results.

Published in:

Control Theory & Applications, IET  (Volume:2 ,  Issue: 5 )